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arXiv:0805.1714 · Physical Review A

Light scattering from a dense and ultracold atomic gas

Igor M. Sokolov, Mariia Kupriyanova, Dmitriy V. Kupriyanov, Mark D. Havey

Published May 7, 2009• 63 citations
arXivHTMLPDF

Abstract

The quantum optical response of high-density ultracold atomic systems is important to a wide range of fundamentally and technically important physical processes. We present here a microscopic analysis of the light scattering on such a system and compare it with a corresponding description based on macroscopic Maxwell theory. Results are discussed in the context of the spectral resonance structure of the scattering cross section, the time-dependent response under a range of conditions, and evolution of these quantities as the atomic density is varied. For high atomic densities, the microscopic theoretical treatment reveals a distributed and configuration-dependent narrow resonance structure. This structure is attributed to microcavity spatial structures associated with the dense and ultracold atomic gases.

DOI
10.1103/physreva.79.053405

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The quantum optical response of high-density ultracold atomic systems is important to a wide range of fundamentally and technically important physical processes. We present here a microscopic analysis of the light scattering on such a system and compare it with a corresponding description based on macroscopic Maxwell theory. Results are discussed in the context of the spectral resonance structure of the scattering cross section, the time-dependent response under a range of conditions, and evolution of these quantities as the atomic density is varied. For high atomic densities, the microscopic theoretical treatment reveals a distributed and configuration-dependent narrow resonance structure. This structure is attributed to microcavity spatial structures associated with the dense and ultracold atomic gases.
We report a combined experimental and theoretical investigation of near-resonance light scattering from a high-density and ultracold atomic 87{}^{87}87Rb gas. The atomic sample, having a peak density $\ensuremath{\sim}$$5\ifmmode\times\else\texttimes\fi{}{10}^{13}$ atoms/cm3{}^{3}3, temperature $\ensuremath{\sim}$65 $\ensuremath{\mu}$K, and initially prepared in the F=1F=1F=1 lower-energy 87{}^{87}87Rb hyperfine component, is optically pumped to the higher-energy F=2F=2F=2 hyperfine level. Measurements are made of the transient hyperfine pumping process and of the time evolution of scattering of near-resonance probe radiation on the $F=2\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=3$ transition. Features of the density, detuning, and temporal dependence of the signals are attributed to the high density and consequent large optical depth of the samples.
Systems of ultracold atoms in optical potentials have taken a place at the forefront of research into many-body atomic systems because of the clean experimental environment they exist in and the tunability of the system parameters. In this thesis we study how light scattered from these ultracold atomic gases reveals information about the state of the atomic gas and also leads to changes in that state.We begin by investigating the angular dependence of light scattered from atoms in optical lattices at finite temperature. We demonstrate how correlations in the superfluid and Mott insulator states affect the scattering pattern, and we show that temperature affects the number of photons scattered. This effect could be used to measure the temperature of the gas, however, we show that when the lattice band structure is taken into account the efficiency of this temperature measurement is reduced.We then investigate light scattering from small optical lattices where the Bose-Hubbard Hamiltonian can be solved exactly. For small lattices, scattering a photon from the atomic system significantly perturbs the atomic system. We develop a model of the evolution of the many-body state that results from the consecutive scattering and detection of photons. This model shows that light scattering pushes the system towards eigenstates of the light scattering measurement process, in some cases leading to a superposition of atomic states.In the second half of this thesis we study light scattering that depends on the internal hyperfine spin state of the atoms, in which case the scattered light can form images of the spatial atomic spin distribution. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. We also show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.We then apply this theory of spin-dependent light scattering to the detection of different spin states of ultracold gases in synthetic magnetic fields. We show that it is possible to distinguish between ground states in the quantum Hall regime using light scattering. Moreover, we show how noise correlation analysis of the spin state images can be used to identify the correlations between atoms and how a variant on phase-contrast imaging can reveal the relationship between the atomic spins.
Based on the developed quantum microscopic theory, the interaction of weak electromagnetic radiation with dense ultracold atomic clouds is described in detail. The differential and total cooperative scattering cross sections are calculated for monochromatic radiation as particular examples of application of the general theory. The angular, spectral, and polarization properties of scattered light are determined. The dependence of these quantities on the sample size and concentration of atoms is studied and the influence of collective effects is analyzed.
We measure the coherent scattering of low-intensity, near-resonant light by a cloud of laser-cooled two-level rubidium atoms with a size comparable to the wavelength of light. We isolate a two-level atomic structure by applying a 300-G magnetic field. We measure both the temporal and the steady-state coherent optical response of the cloud for various detunings of the laser and for atom numbers ranging from 5 to 100. We compare our results to a microscopic coupled-dipole model and to a multimode, paraxial Maxwell-Bloch model. In the low-intensity regime, both models are in excellent agreement, thus validating the Maxwell-Bloch model. Comparing to the data, the models are found in very good agreement for relatively low densities ($n/{k}^{3}\ensuremath{\lesssim}0.1$), while significant deviations start to occur at higher density. This disagreement indicates that light scattering in dense, cold atomic ensembles is still not quantitatively understood, even in pristine experimental conditions.
Light propagation in disordered media is a fundamental and important problem in optics and photonics. In particular, engineering light-matter interaction in disordered cold atomic ensembles is one of the central topics in modern quantum and atomic optics. The collective response of dense atomic gases under light excitation, which crucially depends on the spatial distribution of atoms and the geometry of the ensemble, has important impacts on quantum technologies like quantum sensors, atomic clocks and quantum information storage. Here we analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on the coupled-dipole simulations under different atom number densities and correlation lengths, we show that the collective effects are strongly influenced by those positional correlations, manifested as significant shifts and broadening or narrowing of transmission resonance lines. We also analyze the eigenstate distribution of different atomic ensembles. This work may provide profound implications on collective and cooperative effects in cold atomic ensembles as well as the study of mesoscopic physics concerning light transport in strongly scattering disorder media.
We present the rigorous microscopic quantum theory of the interaction of ultracold Bose and Fermi gases with the electromagnetic field of vacuum and laser photons. The main attention has been paid to the consistent consideration of dynamical dipole-dipole interactions. The theory developed is shown to be consistent with the general principles of the canonical quantization of electromagnetic field in a medium. Starting from the first principles of QED we have derived the general system of Maxwell-Bloch equations for atomic creation and annihilation operators and the propagation equation for the laser field which can be used for the self-consistent analysis of various linear and nonlinear phenomena in atom optics at high densities of the atomic system. All known equations which are used for the description of the behaviour of an ultracold atomic ensemble in a radiation field can be obtained from our general system of equations in a low-density limit.